Be sure and walk up and down Newbury Street in the Back Bay. Lots of shops, and it's its own little architectural tour -- about a decade per block, starting at the Gardens end.
Another great place to walk around is Beacon Hill. Here's what you do: get off the T at Park St -- oldest subway station in America. Walk up Tremont Street toward the State House, then left onto Beacon Street between the gorgeous bow-front houses -- many with original panes of purplish glass -- and Boston Common. Don't miss the memorial to Robert Shaw and the all-black 54th Regiment in the Civil War; it's an impressive work by Saint-Gaudens. Continue as far as Spruce Street and turn into Beacon Hill proper. Right on Chestnut, Left on Walnut, left again on Mt. Vernon. Go down the hill to Louisburg Square, where the REALLY rich people live. Right through the square, right on Pinckney, left on Anderson, left on Myrtle, which curves into Revere Street after a couple of blocks. Revere will take you to Charles Street, the main shopping drag; go left, and you'll end up back at Beacon Street at the dividing point between Boston Common and the Public Gardens. If you're pressed for time, just continue down Mt. Vernon to Charles -- downhill always takes you there if you get lost (bring a map).
If you go to the North End, which you should, make sure you start at the Blackstone Block near City Hall. It's not much -- a couple of tiny blocks behind the Union Oyster House, Scott Alley and Salt Lane, but it's the real old Boston street layout. You come out on Hanover Street, which is the main drag of the North End; turn right and cross the stupid wasteland where the elevated freeway used to be (and shiver at the prospect of doing this to Seattle, as many hope for), until you get to the North End proper on the other side. Be sure to check out some of the side streets. Here: up Hanover to Richmond, turn right and proceed to North Street, turn left and go past Paul Revere's House (1680), left onto Prince Street, then a short and a long block to Salem Street. Turn right on Salem to Hull Street, admire the Old North Church (lovely and plain inside), then left onto Hull Street up the hill to the Copp's Hill Burying Ground. Revolutionary War-era bulletholes in some of the gravestones. Note the 10-foot wide "narrowest house in Boston" across the street from the entrance at #44. Cruise back down Snow Hill Street, left onto Prince again but only for a second, then left onto Thacher Street, left on Cooper Street, which will take you to Salem Street again. Right on Salem past many shops to Cross Street and the former freeway again, where you can cross back into downtown Boston.
Another fascinating corner that few people ever see is Bay Village, a tiny little slice of Beacon Hill that drifted off south of Boston Common. Just a few streets -- Piedmont, Winchester, Melrose, Fayette -- the last two are the prettiest. Go south from Boylston Street Station (also the oldest in the US -- what's a subway without at least two stations?) on Tremont, left onto Stuart, past Charles, left again onto Church Street into Bay Village.
You can combine these walks easily; downtown Boston is really small.